Two-View Analysis

The displacement field computed by the method discussed in the previous chapter provides point correspondences for motion and structure analysis. This chapter deals with estimating motion and structure of the scene from point correspondences between two perspective views. First, an algorithm is presented that computes a closed-form solution for motion and structure parameters. The algorithm exploits redundancy in the data to obtain more reliable estimates in the presence of noise. Then, an approach is introduced to estimating the errors in the computed solution. Specifically, standard deviation of the error is estimated in terms of the variance of the errors in the coordinates of the image points. The estimated errors indicate the reliability of the solution, as well as any degeneracy or near degeneracy that causes the failure of the motion estimation algorithm. The presented approach to error estimation is applicable to a wide variety of problems that involve least-squares optimization or pseudo-inverse. Finally, the relationships between errors and other parameters are analyzed.